Abstract
The purpose of this article is to clarify the relation between the reaction -diffusion models and the integral equation models in the study of the spatial spread of epidemics and to discuss the speeds of spatial spread of an infectious disease through the reaction-diffusion models. The speeds of the epidemic waves are often derived heuristically from the linearization of the model equations, which is called 'the linear conjecture'. For the diffusive Kermack-McKendrick model, we show the validity of the linear conjecture by the use of the existence results of traveling wave solutions. Then, we give an example of the reaction-diffusion epidemic model which has a traveling wave solution with the speed greater than the predicted values of the speed by the linear conjecture, and examine it in the more general setting of reaction-diffusion modeling.
